Bash Shell Script: Building a Better March Madness Bracket

Last year, I wrote an article for Linux Journal titled "Building Your March
Madness Bracket"
My article was timely, arriving just in time for the "March Madness" college
basketball series. You see, I don't follow college basketball (or really, any
sports at all), but I do like to participate in office pools. And every year, it
seems my office likes to fill out the March Madness brackets to see who can
best predict the outcomes.

Since I don't follow college basketball, I am not a good judge of which teams
might perform better than others. But fortunately, the NCAA ranks the teams
for you, so I wrote a Bash script that filled out my March Madness bracket for
me. Since teams were ranked 1–16, I used a "D16" method borrowed from tabletop
gaming. I thought this was an elegant method to predict the outcomes.

But, there's a bug in my script. Specifically, there's an error in a key
assumption for the D16 algorithm, so I'd like to correct that with an improved
March Madness script here.

Let's Review What Went Wrong

My Bash script predicted the outcome of a match by comparing the ranking of
each team. So, you can throw a D16 "die" to determine if team A wins and
another D16 "die" to determine if team B loses, or vice versa. If the two
throws agree, you know the outcome of the game: team A wins and team B loses,
or team A loses and team B wins.

I asserted that a #1 team should be a strong team, so I assumed the #1 team had
15 out of 16 "chances" to win, and one out of 16 "chances" to
lose. Without any other inputs, the #1 ranked team would win if its D16 throw is
two or greater, and the #1 team could lose only if the D16 value was one. With
that assumption, I wrote this function:

In the guesswinner function, each D16 roll generates a random number 1–16. If
the rank of team A is "rankA" and the rank of team B is "rankB," and the D16
roll for team A is "A" and the roll for team B is "B," the function tests two
D16 rolls like this:

If A greater than rankA (team A wins) and B less than or equal to rankB
(team B loses), then team A wins.

If A less than or equal to rankA (team A loses) and B greater rankB (team B
wins), then team B wins.

But look at what happens if team A is ranked #1 and team B is ranked #16. Team
A will always win:

A roll 1–16 will have a 15 out of 16 chance to be greater than 1 (team A
wins), and a 1–16 roll will always be less than or equal to 16 (team B loses).

A roll 1–16 will have a 1 out of 16 chance to be less than or equal to 1
(team A loses) but a 1–16 roll will never be greater than 16 (team B wins).

Jim Hall is an advocate for free and open-source software, best known for his work on the FreeDOS Project, and he also focuses on the usability of open-source software. Jim is the Chief Information Officer at Ramsey County, Minn.